Effects of Deformation-Induced Constraint on High-Cycle Fatigue in Ti Alloys with a Duplex Microstructure
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UCTION
IN recent years, there has been considerable interest in the high-cycle fatigue (HCF) of Ti and Ni alloys, because HCF has been identified as a primary cause of component failure in gas turbine engines in military fighters.[1,2] The damage modes associated with these HCF failures included fretting, foreign object damage, and low-cycle fatigue interaction.[1,2] As part of the United States Air Force material damage tolerance program, the HCF lives of Ti-6Al-4V have been investigated[3–7] as a function of mean stress for Ti-6Al-4V alloys with various processing conditions and microstructures[6,7] in order to investigate possible influence of these variables on HCF lives. The effect of mean stress on HCF life is often presented in terms of the Haigh diagram,[8] which is also referred to as the modified Goodman diagram,[9,10] by plotting the alternating stress or stress amplitude, ra, as a function mean stress, rm, at a constant fatigue life such as 107 cycles. In such a plot, a linear relation between ra and rm is often observed and is referred to as the Goodman line.[10] In general, the relation between alternating stress and mean stress during high-cycle fatigue can be expressed as[10] " # rm d ra ¼ re 1 ½1 rUTS K.S. CHAN, Institute Scientist, and Y.-D. LEE, Principal Engineer, are with the Materials Engineering Department, Southwest Research Institute, San Antonio, TX 78238. Contact e-mail: kchan@ swri.edu Manuscript submitted July 24, 2007. Article published online April 29, 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
where re is the fatigue limit at a fatigue life of 107 cycles, and d is a constant, which has a value of unity in the Goodman relation. Positive deviation from linearity (ra > Goodman line at a given rm) has been observed in many ductile alloys with d = 2 and the resulting equation is often referred to as the Gerber parabola.[10] Instead of using the ultimate tensile strength, the Soderberg line[11] is based on the yield stress, ry, and is obtained by replacing rUTS in Eq. [1] with ry and setting d = 1. The Ti alloys exhibit two different mean stress dependencies of fatigue life, depending on the microstructure.[6,7,12–16] A normal dependence between ra and rm has been observed in a-Ti,[14,15] b-Ti,[14,15] and fully lamellar a + b Ti alloys,[12–15] which include the linear, or parabolic dependence as described by Eq. [1]. In contrast, near-a and a + b Ti alloys with a duplex microstructure consisting of primary a grains and lamellar a + b colonies manifest an anomalous mean stress sensitivity and deviations of ra below the Goodman line (negative deviations).[6,7,12–16] For example, experimental data of Ti-6Al-4V[6,7] appear to show a linear relation between ra and rm for the lamellar a + b microstructure, as shown in Figure 1. For duplex microstructures with primary a grains and lamellar a + b colonies, a nonlinear ra and rm relation with negative deviations (ra < Goodman line at a given rm) is observed. For Ti-6Al-4V, the nonlinear anomalous behavior can be described as bilinear, as show
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